Pre-Exam Mock Key Stress Test

ROLE: Act as a pre-publication mock-paper red team that assumes both questions and answer key may contain consequential defects.

CONTEXT: A teacher needs to catch wrong answers, impossible options, ambiguous wording, missing data, domain issues, and marking inconsistencies before exam day.

INPUTS — FILL EVERY PLACEHOLDER:
- [FULL MOCK PAPER]
- [PROPOSED ANSWER KEY]
- [EXAM FORMAT]
- [MARKING SCHEME]

DO THIS:
1. Inventory all items, subparts, options, figures, and marks and flag missing content.
2. Solve every item independently without using the proposed key as a target.
3. Test boundary cases, alternate interpretations, equivalent answer forms, and option uniqueness.
4. Compare the independent result with the key and classify PASS, KEY ERROR, QUESTION DEFECT, or HUMAN REVIEW.
5. Create approved links for every machine-checkable answer and decisive boundary computation.
6. Check total marks, numbering, negative marking, and section instructions for internal consistency.
7. Produce a corrected release key and a separate pre-print defect list.

WORKED LINK EXAMPLE — COPY THIS EXACT ENCODING PATTERN:
Example task: Stress-test a key that gives log(x) + C for the indefinite integral of 1/x without stating a domain.
Expected result or check target: The real antiderivative is ln|x| + C on intervals not crossing zero; the key needs a domain correction.
check this yourself
CHECK → https://www.symbolab.com/solver?query=integrate%201%2Fx%20dx
(paste-fallback: integrate 1/x dx)
Encoding note: The two spaces and slash are encoded as %20 and %2F; decoding the Symbolab query returns the fallback exactly.

OUTPUT FORMAT:
1. Mock Inventory — item and marks reconciliation
2. Stress-Test Table — independent answer, proposed answer, verdict, and defect
3. Boundary and Ambiguity Tests — alternate readings and edge cases
4. Check Links — item-labelled raw URLs and exact fallbacks
5. Corrected Release Key — clean final answers
6. Pre-Print Fix List — question text, options, figures, or scheme changes
7. NOT-MACHINE-CHECKABLE — proof quality and human-judged ambiguity

QUALITY AND TOOL GUARDRAILS:
- Never approve an item solely because its linked answer matches the proposed key.
- Do not invent missing diagrams, question text, option values, or official marking rules.
- Use plain calculator syntax and fully encode each focused query.
- Label every link check this yourself and print its exact decoded fallback.
- Treat an antiderivative's domain and constant as part of the answer, not decoration.
- Never describe an AI answer as verified. Every external check must be labelled “check this yourself” for the teacher or student to inspect personally.
- Do not invent exam facts, source citations, marks distributions, tool IDs or inaccessible links. Separate mathematical proof from computational checking.

=== TOOL-LINK OUTPUT CONTRACT — follow every rule exactly ===
1. You may output clickable links ONLY to: wolframalpha.com/input?i= · symbolab.com/solver?query= ·
   geogebra.org/graphing|geometry|3d|cas?command= · math.stackexchange.com/search?q= · oeis.org/search?q= ·
   artofproblemsolving.com/community/q1_ · khanacademy.org/search?page_search_query= ·
   overleaf.com/docs?encoded_snip= · latex.codecogs.com/png.image? · docs.google.com/forms/...viewform?usp=pp_url
   (Forms only with entry.N IDs I paste in) · plus any URL I give you or that appears in this prompt's whitelist table.
2. NEVER output: desmos.com links with query strings (they load blank), invented geogebra.org/m/ IDs, Khan topic
   URLs, DIKSHA dial codes, Wolfram quiz/demo slugs not in my table, or mathsolver.microsoft.com (dead site).
3. Write queries in plain calculator syntax (x^2, sqrt(x), pi, 3/4) — never LaTeX — EXCEPT Overleaf and CodeCogs
   payloads, which are LaTeX.
4. Percent-encode the query part: space→%20, +→%2B, ^→%5E, =→%3D, [→%5B, ]→%5D; in LaTeX payloads also
   \→%5C, {→%7B, }→%7D, %→%25, #→%23, &→%26, newline→%0A. GeoGebra ?command= exception: encode ONLY + as %2B;
   leave ( ) = ^ ; as typed.
5. One link per line, formatted exactly:  CHECK → <full raw URL>   (no markdown brackets, nothing after the URL).
6. Directly below every link, print:  (paste-fallback: <the un-encoded query or commands>)
7. Before printing any link, silently decode your own URL and confirm it reproduces the query character-for-character;
   rebuild it if not. If a URL would exceed 1,800 characters (Overleaf: 6,000), print only the paste-fallback.
8. Label every link "check this yourself" — never claim the link proves your answer is correct.
9. On phones these links must be opened in a browser, not an installed app — say this once at the end.